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Popular >

ln(9e^{2x})=1

Solution

ln (9 e^{2 x}) = 1

Solution

x = \frac{1 - 2 ln ( 3 )}{2}

+1

Decimal

x = - 0.59861 \dots

Solution steps

ln (9 e^{2 x}) = 1

Rewrite the equation with

e^{2 x} = u

ln (9 u) = 1

Solve

ln (9 u) = 1 : u = \frac{e}{9}

u = \frac{e}{9}

Substitute back

u = e^{2 x},

solve for

x

Solve

e^{2 x} = \frac{e}{9} : x = \frac{1 - 2 ln ( 3 )}{2}

x = \frac{1 - 2 ln ( 3 )}{2}

Graph

Popular Examples

30+50e^{-0.2x}=40

30 + 50 e^{- 0.2 x} = 40

3\times 4e^{2-2x}+1=4

3 \times 4 e^{2 - 2 x} + 1 = 4

1 0^{\frac{x}{4}} = 3

e^{2x}+2e^{2x}x=0

e^{2 x} + 2 e^{2 x} x = 0

1000 e^{- 4 x} = 75

Frequently Asked Questions (FAQ)

What is the answer to ln(9e^{2x})=1 ?
The answer to ln(9e^{2x})=1 is x=(1-2ln(3))/2